Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. Angle $b$ and the $146^{\circ}$ angle are vertical angles. So $b = 146^{\circ}$.

Step2: Use linear - pair property

Angles $b$ and $c$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $c=180^{\circ}-b$. Substitute $b = 146^{\circ}$ into the equation: $c = 180 - 146=34^{\circ}$.

Answer:

$b = 146^{\circ}$, $c = 34^{\circ}$